1. American Eagle
First Hill

2. Motion (Acceleration)
Prediction:
Acceleration = -7 m/s2 at
bottom of hill b/c while the
coaster is close to free
fall, it does not go straight
down so its acceleration
would be smaller than -
9.8m/s2.

3. Method 1 (Accel.)
Vertical
acceleration
graph from vest
data (Y-accel.
graph)
Acceleration =
-7.1 m/s2

4. Error Analysis/ Confidence
 We could have misread/misinterpreted the results on data studio
 Person who collected data could have shifted, thereby affecting
the results
 We are confident in our data because aside
from the results supporting our
hypothesis, the vest data seems to be fairly
consistent without any major bumps
Errors that could have occurred include:

5. Measure cars and distance between cars in shoe
lengths (shoe = .3m)
Time how long it takes for the cars to pass a point on
bottom and top of first drop
Find velocity at top and bottom (V= Δx/Δt)
Time how long it takes to get from top to bottom and
divide difference in velocities by time (from top to
bottom) to get acceleration.
Method 2 (Accel.)

6. Car
Lengt
h
(shoes
)
Gap
Lengt
h
(shoes
)
Total
Lengt
h (m)
Time
to
pass A
(sec)
Time
to
pass B
(sec)
Time
from
A to B
(sec)
Vel. At
A
(m/s)
Vel. At
B
(m/s)
Accel.
(m/s2)
Trial 1 8.5 2 15.15 2.49 .7 3.05 6.08 21.64 -5.101
Trial 2 8.25 2 14.775 2.43 .65 3.11 6.08 22.73 -5.354
Trial 3 8.5 2 15.15 2.51 .81 2.98 6.04 18.70 -4.248
Table (Method 2)

7. Method 2 (Math)
TOTAL TRAIN LENGTH
Trial 1- (8.5*.3)(5)+(2*.3)(4)= 15.15m
Trial 2- (8.25*.3)(5)+(2*.3)(4)=14.775m
Trial 3- (8.5*.3)(5)+(2*.3)(4)= 15.15m
VELOCITY AT A (TOP)
Trial 1- 15.15/2.49=6.08m/s
Trial 2- 14.775/2.43=6.08m/s
Trial 3- 15.15/2.51=6.04m/s
VELOCITY AT B (BOTTOM)
Trial 1- 15.15/.7=21.64m/s
Trial 2- 14.775/.65= 22.73m/s
Trial 3- 15.15/.81=18.70m/s
ACCELERATION ON FIRST DROP
Trial 1- (6.08-21.64)/3.05=
-5.101m/s2
Trial 2- (6.08-22.73)/3.11=
-5.354m/s2
Trial 3- (6.04-18.70)/2.98= -
4.248m/s2
Avrg. Accel. = -4.90 m/s2
Avrg. Time = 3.05 s

8. Error Analysis
Errors that may have occurred:
 Time may have been measured incorrectly due to lack of perfect
location for spotting first drop and lack fast reaction time-> time
may have been a few seconds off
 Since a different shoe was used during actual experimentation, the
total train length may have been affected, therefore affecting the
velocity and acceleration
 The foot length may have not been the exact measurement

9. Confidence
 We are not confident with the data for this
method because not only does it refute our
hypothesis, the percent error is nearly %40
off.
 Since each method provided different
results, we are not very confident in our data

10. Conclusion
• We hypothesized that the acceleration at the bottom of the hill would be -7
m/s2
• While one of our methods resulted in an acceleration of -7.1 m/s2, our second
method resulted in an acceleration of -4.9 m/s2, and therefore , our data does
not support our hypothesis
• In order to improve our data, factors we’d take in to consideration are:
 Find a location in which we can easily spot and time the first
drop
 Use the same shoe during the prelab data collection and
during the actual experimentation so no other factors are
affected
 More trials could have been conducted

11. Engineering & Height
Prediction: We estimated
the drop to be 50 meters
high because it seems to be
about that high.

12. Find height w/ altitude graph (vest data)
Measurement at top minus measurement at bottom
to obtain height of coaster track
Method 1 (Engin. & Height)

13. Method 1 (Altitude Graph)

14. Height at top= 38m
Height at bottom= -11m (coaster starts above ground
level)
38-(-11)= 49m
49TOTAL HEIGHT FROM TOP OF FIRST DROP
Method 1 (Math)

15. Error Analysis/ Confidence
Errors that could have occurred include:
• We could have misread/misinterpreted the graph, thereby
affecting our results
• The person wearing the data vest could have not been sitting
in an upright position and may have shifted while on the
ride, therefore affecting the results

16. Confidence
We are confident in our data for this method
because not only does our results support our
hypothesis, but it is difficult to get incorrect
data while using the data vest

17. Triangulation Formula:
(sinӨ1)(sinӨ2)/(sin(Ө1-Ө2))*B+ eye height
*Find angles w/ horizontal accelerometer and baseline
of 20m using 5m string to measure
*Eye height= 1.47 (meter stick measurements)
Method 2 (Engin. & Height)

18. Ө1
(degrees)
Ө2
(degrees)
Baseline
(m)
Eye
Height
(m)
Height
(m)
Trial 1 25 20 20 1.47 34.64
Trial 2 23 20 20 1.47 52.539
Trial 3 24 17 20 1.47 20.95
Method 2 Triang. Chart
Average Height: 35.87 m

19. Error Analysis
Errors that could have occurred include:
 When we used the horizontal accelerometer, we may have
not have been looking at the top of the drop
 While measuring the baseline, other students in line may
have gotten in the way, and therefore our baseline may not
have been exactly 20 m in a straight line
 When measuring our baseline, we may have not held the
string to its fullest length, and therefore our baseline may
have been less than 20 m
 While measuring the 1st and 2nd angle, we may have not
looked at the exact point
 The measurements using the horizontal accelerometer may
have been slightly off because not only did it measure every
5 degrees, the marbles occasionally got stuck in the tube

20. Confidence
We are not confident with our data
because not only do our results not
support our hypothesis, the percent
error is about 40%.

21. Conclusion
 We hypothesized that the height at the top of the first drop would be 50 m
 Our data does not support our hypothesis because although one of our
methods resulted in 49 m, the second method resulted in 35.87 m
 In order to improve our results, factors we would consider include:
 Possibly conduct multiple trials with different eye heights
as opposed to using one person for all three trials
 Measure the baseline and angles more carefully

22. Prediction: GPE at top of hill = KE at bottom because
energy is conserved.
Energy (GPE~KE)
g-field
GPE
GPE
Car
Halfway
Down
Top
KE
g-field
Car
KE
Bottom

23. Use height from engineering/height portion and plug
that into GPE formula: GPE= mgΔy to find GPE at top
of hill
Use velocity value obtained from motion portion and
mass of group member to find KE at bottom of hill
using KE equation: KE= 1/2mv2
Method 1 (Energy)

24. Method 1 (GPE)
Height (m) Mass (kg)
35.87 52.27
GPE= mgΔy
GPE= (52.27)(9.8)(35.87)
GPE= 18,374.26 Joules

25. Method 1 (KE)
Velocity (m/s) Mass (kg)
-14.95 52.27 kg
KE= 1/2mv2
KE= 1/2(52.27)(-14.95)2
KE= 5,841.24 Joules
V = at
V = (-4.90)(3.05)
V = -14.95 m/s

26. Error Analysis/ Confidence
Errors that could have occurred include:
 The velocity and height that we found in the previous
slides may have been incorrect, therefore affecting our
results
We are not confident in our data for
this method because the GPE at the
top of the drop is not at all similar to
the KE at the bottom

27. Use the GPE and KE equations to find out GPE at top
of hill and KE at bottom of hill
Receive height value from vest data
Receive velocity from area under acceleration graph
from vest data
Method 2 (Energy)

28. Method 2 (GPE)
Height (m) Mass (kg)
49 52.27
GPE= mgΔy
GPE= (52.27)(9.8)(49)
GPE= 24,843.9 Joules

29. Method 2 (KE)
Velocity (m/s) Mass (kg)
-23.52 52.27
KE= 1/2mv2
KE= ½(52.27)(-23.52)2
KE= 14,457.6 Joules

30. Error Analysis/ Confidence
Errors that could have occurred include:
o The vest data we used could have been incorrect due to
the fact the rider who collected this data may have
shifted, therefore affecting our height and velocity
o We could have misread the vest data, thereby affecting
our results
We are not confident in our data for
this method because the GPE at the
top of the drop is not at all similar to
the KE at the bottom

31. Conclusion
 We hypothesized that the KE at the top of the hill would be equal to the
GPE at the bottom of the hill
 Our data does not support our hypothesis because for each method we
used, not one posed similar results for the KE at the top and the GPE at
the bottom
 In order to improve the results of our experiment, factors we could
consider include:
 Conduct more trials
 Measure angles and baseline more carefully-> could
have affected the height we used
 Time the train more carefully to get a more accurate
velocity

32. Forces
Prediction: Bottom of
hill/drop Fs will be about 2.5
times Fg because it takes a
lot of force to change the
motion of the roller coaster
train and we estimate it to
be about 2.5Fg.
Y
X
Fs
Fg

33. Use data vest
Look at y-directional acceleration graph and find
value at bottom of hill
Divide by 9.8 to get the factor of Fg, because mass is
constant, it can be ignored.
Method 1 (Forces)

34. Method 1 (Graph)

35. Y-acceleration=27.5
27.5/9.8=2.81
Fs=2.81Fg
Method 1

36. Error Analysis/ Confidence
Errors that could have occurred include:
 The vest data could have been incorrect
 We could have misread the vest data
 We are not confident in our hypothesis b/c vest data is
much more reliable than our hypothesis

37. Method 2 (F0rces)
Use vertical
accelerometer to get
value for y-acceleration
which is already in terms
of Fg.
Accelerometer
Reading
Trial 1 2.75 Fg
Trial 2 2 Fg

38. Error Analysis/ Confidence
 We are relatively confident in our data because when we
average all of our results, we end up with an average of
Fs=2.52Fg, which is very close to our hypothesis of 2.5Fg.
 Some errors that could have occurred are:
 Difficulty to read accelerometer while on roller coaster.
 Bouncing spring
 Not enough trials to get a good average

39. Conclusion
 We hypothesized that the Fs at the bottom of the hill/ drop will be
about 2.5 times Fg
 Our data does not support
 If we were to improve upon our data, factors we would take into
consideration include:
 More carefully read the vertical accelerometer
 Conduct more trials (even if that means going on
the ride more than 2 times)